Rotor Calibration Procedure

The rotor calibration experiment is the first set of data all UltraScan-III users should acquire for their own rotor and instrument. Titanium rotors used in the Beckman Analytical Ultracentrifuge will stretch as a function of rotor speed, temperature, age and type of centerpieces loaded in them. Since the stretching will translocate the position of each centerpiece and cell, the forces acting on the sedimenting particles will also change as a function of stretching (due to the increased radius, the force increases) and the bottom of the cell, which is a boundary condition of the ASTFEM Lamm equation solution, will also change. To obtain optimal fitting results, it is important that the rotor stretch and centerpiece geometry is properly accounted for in the analysis software. UltraScan-III contains a rotor calibration program that allows you to easily determine your rotor's particular rotor stretching function, and to incorporate this information automatically in the analysis routines in UltraScan. The idea is that you run a calibration experiment where the stretching of the rotor is measured on your instrument, and then these data are fitted to a rotor stretching function, which is then stored in the program and used to provide, in combination with the known centerpiece geometry, the correct boundary conditions for the ASTFEM solutions.

Step 1: Measurement of the calibration data

To measure the calibration data, select the centerpieces and rotor to be calibrated and make sure that the centerpieces and counterbalance are properly balanced. An imbalance in the rotor may cause tilting, and deteriorate the sharpness of the centerpiece corners since they are no longer vertical. It is recommended to leave the centerpieces empty. Use fully assembled cells in the 4 hole rotor and 7 in the 8 hole rotor, and insert the counterbalance. Program a methods scan in the Beckman data acquisition software with the following settings:

Step 2: Convert Legacy Data

Import the data into UltraScan-III with the "Convert Legacy Data" function in the "Utilities" menu. Create a new rotor with the rotor utility under "Edit Run Information", "Select Lab/Rotor/Calibration" with the "Add new Rotor function. Select a default dummy rotor calibration, since you don't have a valid calibration yet. The dummy calibration is based on the calibration of one of our rotors, and is probably fairly typical for all Beckman rotors, but it is worth it to get your own calibration to make sure the data are optimal. Later on, you will be able to replace the dummy calibration with your own calibration so it can be picked by default. More information on the rotor calibration routine can be found in the Rotor Information manual page of UltraScan-III. Proceed with the legacy data conversion as described in the UltraScan-III Manual. Since the data are acquired in intensity mode you should also convert the data to pseudo-absorbance.

Step 3: Calculate the rotor calibration

Load the data into the UltraScan-III "Rotor calibration " program in the "Utilities" menu. The program will show alternating views of the intensity profiles for top and bottom, and channel A and channel B. So, each cell will provide four sets of calibration data for the rotor stretch. These data also are used to calculate average dimensions for the cells and the center position at rest. This position should be at 6.500 cm. A consistent deviation of this number could reflect an incorrect radial calibration file for your instrument. The top of each channel is shown in red, and the bottom of each channel is shown in green. Using the mouse, draw a rectangle around the most vertical section of each plot as shown in this figure. Repeat until all cells and the counterbalance have been processed. When the last counterbalance corner has been defined, a calibration profile will appear on the screen and the calibration information can be viewed:

PERFORMED ON: Tue Sep 20 11:23:57 2011

Calibration is based on data from run: SN341_titanium

The following equation was fitted to the measured stretch values for this rotor:

Stretch = -7.80737e-17 + 9.29165e-08 rpm + 7.48845e-12 rpm^2

Below is a listing of the stretching values as a function of speed:

Speed: Stretch (cm): Standard Dev.:
    0   0.00000e+00   0.00000e+00
 4000   1.74866e-04   8.20738e-04
 5000   4.14449e-04   1.01801e-03
 6000   6.54032e-04   1.26089e-03
 7000   9.24866e-04   1.43976e-03
 8000   1.04726e-03   1.64830e-03
 9000   1.00820e-03   1.73305e-03
10000   1.28945e-03   1.69376e-03
11000   1.67487e-03   1.56125e-03
12000   2.09153e-03   1.58443e-03
13000   2.58112e-03   1.25065e-03
14000   2.71653e-03   1.08573e-03
15000   2.78528e-03   1.96194e-03
16000   2.98505e-03   2.02843e-03
17000   3.23737e-03   2.01287e-03
18000   3.69310e-03   1.96966e-03
19000   3.82450e-03   1.78683e-03
20000   4.41445e-03   2.04758e-03
21000   4.63618e-03   1.95171e-03
22000   5.10716e-03   2.01561e-03
23000   5.83112e-03   1.45173e-03
24000   6.27209e-03   1.29748e-03
25000   6.46802e-03   1.85930e-03
26000   6.95612e-03   2.08601e-03
27000   7.70128e-03   1.95180e-03
28000   8.06028e-03   1.87010e-03
29000   8.58856e-03   1.71424e-03
30000   9.17278e-03   1.70367e-03
31000   9.90403e-03   1.96221e-03
32000   1.04394e-02   2.04542e-03
33000   1.08519e-02   1.96936e-03
34000   1.14603e-02   1.75098e-03
35000   1.15915e-02   2.29961e-03
36000   1.23728e-02   2.13577e-03
37000   1.31280e-02   2.19349e-03
38000   1.35850e-02   2.27936e-03
39000   1.43311e-02   2.15942e-03
40000   1.51540e-02   2.25530e-03
41000   1.54467e-02   2.28450e-03
42000   1.63226e-02   2.34292e-03
43000   1.67269e-02   2.43400e-03
44000   1.75082e-02   2.36511e-03
45000   1.83311e-02   1.96229e-03
46000   1.92721e-02   1.83281e-03
47000   1.99642e-02   2.45517e-03
48000   2.05603e-02   2.33275e-03
49000   2.16749e-02   2.57997e-03
50000   2.23441e-02   2.32618e-03
51000   2.35918e-02   2.42400e-03
52000   2.41957e-02   2.20941e-03
53000   2.50186e-02   2.46008e-03
54000   2.61228e-02   2.47292e-03
55000   2.70794e-02   2.44107e-03
56000   2.78120e-02   2.64401e-03
57000   2.88728e-02   2.39626e-03
58000   2.96340e-02   2.61832e-03
59000   3.07429e-02   2.65833e-03
60000   3.15603e-02   2.54693e-03

Based on these stretching factors, the bottom of each 
cell and channel at rest is estimated to be as follows:

Cell: Channel:     Top:       Bottom:     Length:       Center:

 1       1      5.92140e+00 7.12664e+00 1.20524e+00 6.52402e+00
 1       2      5.91678e+00 7.12212e+00 1.20534e+00 6.51945e+00
 2       1      5.91072e+00 7.11437e+00 1.20366e+00 6.51254e+00
 2       2      5.91683e+00 7.11854e+00 1.20171e+00 6.51769e+00
 3       1      5.91932e+00 7.12065e+00 1.20133e+00 6.51999e+00
 3       2      5.92020e+00 7.12140e+00 1.20120e+00 6.52080e+00
 4       1      5.97527e+00 7.11344e+00 1.13817e+00 6.54435e+00
 4       2      5.99732e+00 7.13543e+00 1.13810e+00 6.56637e+00
Avgs. for CPs:  5.91754e+00 7.12062e+00 1.20308e+00 6.51908e+00

In this example, the center position for cells 1-3 all show a consistent drift to the right, with about 0.02 cm offset from center. There are three possible reasons for this:

  1. the cell housings are worn out and the centerpiece is not correctly positioned in the center of the rotor hole
  2. the rotor calibration file has inaccurate calibration information
  3. the cell has not been properly aligned and the centerpiece is not correctly positioned in the rotor hole.

When the bottom positions are significantly different for each channel of a cell, the cell may be misaligned in the rotor, When the bottom position at rest does not agree with the measured values for each centerpiece, then the calibration file is most likely inaccurate, or the cell housing is worn out.

Step 4: Associate the rotor calibration with the right rotor

Once you are satisfied with the rotor calibration profile (here is an example of a good calibration profile) you can associate it with your rotor in the Rotor Calibration program of UltraScan-III as described in this UltraScan-III Manual page.